Harold Coxeter, 96, Who Found Profound Beauty in Geometry

By STUART LAVIETES

Published: April 7, 2003

Dr. Harold Scott MacDonald Coxeter, a mathematician who was hailed as one of the foremost geometricians of his generation and whose ideas inspired the drawings of M. C. Escher and influenced the architecture of R. Buckminster Fuller, died on March 31 in his home in Toronto. He was 96.

Dr. Coxeter, whose childhood fascination with symmetry led to his career in mathematics, was driven by the idea that beautiful explanations exist for all puzzles. Several mathematical concepts have been named for him, including Coxeter groups.

He also made major contributions to the theory of polytopes, which are complex objects of more than three dimensions that, while not existing in the real world, can be described mathematically.

Dr. Coxeter met M. C. Escher in 1954 at a mathematics conference in Amsterdam. Escher, a Dutch artist who had grown tired of repeating images of birds and fish on a flat plane, had heard about Dr. Coxeter's work on shapes in multidimensional space and sought him out.

After the conference, Dr. Coxeter sent him a copy of his paper ''Crystal Symmetry and Its Generalizations,'' which was illustrated with complex geometric figures, including a circle containing a pattern of objects that grew smaller and smaller as they neared the edge.

Inspired, Escher used this figure as a source for his series of ''Circle Limit'' etchings. Many of his most famous works, including ''Ascending and Descending,'' his 1960 illusion of interlocking staircases, reflect Dr. Coxeter's ideas about polytopes.

Dr. Coxeter and Escher remained friends until the artist's death in 1972. In 1996, Dr. Coxeter published a paper proving that Escher's ''Circle Limit III'' was mathematically perfect.

Dr. Coxeter was also friendly with R. Buckminster Fuller, who cited the influence of Dr. Coxeter's ideas on the development of the geodesic dome. Mr. Fuller dedicated his book ''Synergetics'' to Dr. Coxeter.

Harold Scott McDonald Coxeter, known as Donald, was born in London. A child musical prodigy, he was an accomplished pianist who composed various pieces for the piano, a string quartet and at the age of 12 an opera.

As a student at Cambridge, he was one of five students selected by Ludwig Wittgenstein to attend his philosophy of mathematics classes. He received his undergraduate and doctorate degrees from the university.

In 1936, Dr. Coxeter accepted a a position at the University of Toronto and remained there until his death.

He published more than 200 articles and wrote 12 books, including Non-Euclidean Geometry (1942); Introduction to Geometry (1961), which became a Book of the Month Club selection; and Regular Complex Polytopes (1974).

He also revised and rewrote many editions of Mathematical Recreations and Essays, a series originally published in the 19th century.

Dr. Coxeter's wife, Hendrina, died in 1999. He is survived by a daughter, Susan Thomas, and a son, Edgar.

Attributing his longevity to vegetarianism and a daily regimen of 50 push-ups, Dr. Coxeter traveled to a conference in Budapest in July 2002 to deliver an address on hyperbolic geometry.

According to John Bland of the University of Toronto's math department, he had just completed the final touches on his last paper.